In a letter to a fellow physicist in 1915, Albert Einstein described how a scientist gets things wrong:

“1. The devil leads him by the nose with a false hypothesis. (For this he deserves our pity.)

“2. His arguments are erroneous and sloppy. (For this he deserves a beating.)”

According to his own rules, Einstein should have been pitied and beaten alike. “Einstein himself certainly committed errors of both types,” the astrophysicist Mario Livio writes in his enlightening new book, “Brilliant Blunders.”

Much of what we read about science is some version of a success story: Scientists just discovered the oldest human fossil; how did they do it? Success is certainly part of the story, but this version of Whig history blinds us to how people actually do science. Science is a mess. It’s shaped by the time and place in which scientists work. Scientists choose to do a certain experiment or interpret an observation for many reasons. “More than 20 percent of Einstein’s original papers contain mistakes of some sort,” Livio writes. “In several cases, even though he made mistakes along the way, the final result is still correct. This is often the hallmark of great theorists: They are guided by intuition more than by formalism.”

For many people, however, being a great scientist means being above error. That’s why it is so common to see a magazine cover headline declaring, in screaming type, Einstein was wrong, or its weasel-word variant, was Einstein wrong?

Livio’s book is a valuable antidote to this skewed picture. He profiles five great scientists — Einstein, Charles Darwin, Lord Kelvin, Linus Pauling and Fred Hoyle — each of whom made major discoveries and major mistakes. All five put their chips down on the wrong number, even as others prevailed. Thanks to his deep curiosity, Livio turns “Brilliant Blunders” into a thoughtful meditation on the course of science itself.

When Charles Darwin presented his theory of evolution in 1859, he built a foundation for all of modern biology. Crucial to his theory was the fact that animals and plants inherited traits from their ancestors. Natural selection favored some traits over others, giving rise to long-term change. But Darwin didn’t know how heredity worked. He devoted a lot of time to developing ideas that, in hindsight, seem daft. “Darwin had been educated according to the then widely held belief that the characteristics of the two parents become physically blended in their offspring,” Livio writes, “as in the mixing of paints.” By this logic, each ancestor’s genetic contribution would be halved in each generation.

This idea wasn’t just wrong. It undermined Darwin’s own theory of evolution. If our traits are just a result of blended particles, it shouldn’t be possible for natural selection to change traits over the generations. But try as he might, Darwin couldn’t figure out a better explanation.

Yet right around the time that Darwin published “On the Origin of Species,” the Czech monk Gregor Mendel was discovering genetics. Crossing pea plants in his garden, he got a glimpse at how heredity actually does work. Darwin apparently never became aware of Mendel’s work, nor did he discover Mendel’s results for himself.

Today biologists can track evolution at the molecular level because they know what genes are made of. In the early 1950s, Francis Crick and James Watson worked out the double-helix structure of DNA. They worked quickly, because they knew that the Nobel Prize-winning biochemist Linus Pauling was trying to solve the puzzle as well. Pauling came very close, but stumbled just as Watson and Crick were making their breakthrough. He got stuck on the idea that DNA forms three intertwined spirals, rather than two, and worse, he made an elementary error in the chemistry — his nucleic acid molecule was actually not an acid.

Shortly after Crick and Watson published their discoveries in 1953, Pauling paid them a visit at Cambridge and examined their model of DNA. He acknowledged that they were right and he was wrong, and soon afterward he made the same declaration in public. That kind of graciousness is not universal among Livio’s blunderers, though. The great physicist Lord Kelvin held firm, until his death in 1907, to his conviction that the Earth was only millions of years old.

Kelvin believed that life had been designed, and he investigated the age of the Earth in part to rebut Darwin’s theory of natural selection. If Darwin’s theories were right, then the Earth must be very old, but geologists had no way to precisely measure the planet’s age. Kelvin had the brilliant insight that the temperature of rocks might hold the answer.

The Earth, Kelvin rightly reasoned, had started out as a ball of molten rock. It took a straightforward mathematical exercise to calculate how long it had taken for the Earth to cool to its current temperature. And when Kelvin did the math, he concluded that the Earth was fairly young, roughly 100 million years (we now know it to be about 4.567 billion years old). He carried out similar calculations to work out the comparable age of the Sun. If the Sun had indeed formed billions of years ago, Kelvin believed it would have burned out long ago.

Kelvin was wrong for two reasons. As a former student of his pointed out, Kelvin assumed that the Earth’s interior was fixed and transports heat at the same rate everywhere. In fact, it roils like boiling water, transporting heat to the surface. The other reason for Kelvin’s error was quantum physics. Radioactivity helps keep the Earth warm, and nuclear fusion has allowed the Sun to burn for 4.567 billion years. Kelvin’s critics brought both these counterarguments to his attention, but he seems to have viewed them with contemptuous indifference.

Nuclear fusion doesn’t just power stars, it also creates new elements like carbon and iron. The British astrophysicist Fred Hoyle made this tremendous discovery in the 1940s and ’50s. Unfortunately, Hoyle might be better known for promoting a flawed theory about the origin of the universe: He was convinced that the universe was in a continual state of creation. As evidence for the Big Bang mounted, he became an increasingly embarrassing crank.

Livio chooses Einstein as the fifth member of his blundering quintet. Einstein was puzzled as to why the universe didn’t cave in on itself. Empty space, he suggested, contained a mysterious energy pushing outward, resisting the universe’s inward collapse. After he published this idea — what came to be known as the cosmological constant — he regretted it. He said it didn’t emerge naturally from his equations; he’d tacked it on like a cheap piece of plywood over a hole in a roof.

Einstein eventually denounced the cosmological constant. And that, it turns out, was his big mistake. In the 1990s, physicists discovered dark energy, something very similar to that mythical force.

Livio brings the care of a historian to his nimble narratives, avoiding heroic clichés. He’s less adept at explaining why these great scientists made their mistakes, too often trotting out pop psychology to demonstrate why people stubbornly cling to ideas even when they see evidence to the contrary. The psychology of bad science is a fascinating topic, but it requires a broader look at how the entire scientific community operates. Five scientists — no matter how great — cannot shoulder that load.

Copyright 2013 The New York Times Company. Reproduced with permission.